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Both of the right triangular prisms shown have bases that are right triangles with hypotenuse length 10 cm. One prism has height x and a base leg of length 6 cm. The other prism has height x - 2 cm and a base leg of length 5*sqrt(2) cm. The prism with height x - 2 cm has a volume that is 75% the volume of the prism of height x. What is the value of x? 

 Jul 12, 2022
 #1
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First prism

Other leg length  =  sqrt (10^2 - 6^2)   =sqrt (64)  = 8

Volume of this  prism =  base area * height =  (1/2) (6 * 8)  * x =  24x

 

Second prism

Other leg length = sqrt (10^2 - 50)  =sqrt (50)

Volume of this prism (1/2) (sqrt 50)^2 * ( x - 2 ) =   25 ( x - 2)

 

And we know that

 

.75 (24x)  = 25 ( x - 2)

 

18x = 25x - 50                rearrange as

 

25x - 18x  =  50

 

7x = 50

 

x =  50 /  7

 

 

cool cool cool

 Jul 12, 2022

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